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GPS and relativity
Intermediate
Satellites must correct for both special and general relativistic effects.
GPS satellites orbit at 14,000 km/h; special relativity slows their clocks by 7 μs/day while weaker gravity speeds them by 45 μs/day. Net +38 μs/day would accumulate 10 km position error daily without corrections.
Corrected by offsetting the clock frequency.
Both effects matter.
In more detail
GPS satellites experience both special relativistic time dilation from their speed and gravitational time dilation from their altitude. Their clocks run faster by about 45 microseconds per day after correction for these effects.
Real-world uses
- Navigation systems depend on accurate timing corrected by relativity.
- Relativistic corrections allow global positioning to within metres.
- GPS receivers must correct for both special relativistic and general relativistic effects to give metre-level accuracy.
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Frequently asked questions
Which effect dominates?
Gravitational time dilation is larger, so satellite clocks run faster than ground clocks.
What happens without corrections?
Position errors would grow by about 10 kilometres per day.
How big is the GPS time correction?
Without corrections, the position error would grow by roughly ten kilometres each day.
Related topics in Relativity
Equivalence principle · Gravitational time dilation · Gravitational redshift · Curved spacetime · Einstein field equations · Geodesics